# Math Help - Negative Exponents

1. ## Negative Exponents

Consider the following:

$7/x^-^5^/^6$

To express the above with a positive index i.e. to make the the exponent -5/6 positive, we need to do the reciprocal which will be

$1/7/x^-^5^/^6$

which comes to

$x^5^/^6/7$

But the correct answer is

$7x^5^/^6$

Why?

Thanks,

Ron

2. 7 / x^(-5/6)
= [7 / x^(-5/6)] * [x^(5/6) / x^(5/6)] : multiplication by 1
= [7 x^(5/6)] / [x^(-5/6) x^(5/6)]
= [7 x^(5/6)] / x^0
= 7 x^(5/6)